Decomposition has been the mainstream approach in the classic mathematical programming for multi-objective optimization and multi-criterion decision-making. However, it was not properly studied in the context of evolutionary multi-objective optimization until the development of multi-objective evolutionary algorithm based on decomposition (MOEA/D). In this article, we present a comprehensive survey of the development of MOEA/D from its origin to the current state-of-the-art approaches. In order to be self-contained, we start with a step-by-step tutorial that aims to help a novice quickly get onto the working mechanism of MOEA/D. Then, selected major developments of MOEA/D are reviewed according to its core design components including weight vector settings, sub-problem formulations, selection mechanisms and reproduction operators. Besides, we also overviews some further developments for constraint handling, computationally expensive objective functions, preference incorporation, and real-world applications. In the final part, we shed some lights on emerging directions for future developments.
翻译:在传统的数学编程中,分解一直是用于多目标优化和多标准决策的主流方法,然而,在根据分解法(MOEA/D)制定多目标进化算法之前,在进化多目标优化方面没有进行适当研究。在本条中,我们全面调查了MOEA/D从起源到目前最先进的方法的发展情况。为了实现自足,我们首先进行逐步的辅导,目的是帮助新手迅速进入MOEA/D的工作机制。然后,对MOEA/D的选定主要发展动态根据其核心设计组成部分进行审查,包括重量矢量设置、次问题配方、选择机制和再生操作者。此外,我们还概述了制约处理、计算昂贵的客观功能、优惠结合和实际应用方面的一些进一步动态。最后,我们为未来发展的新方向提供了一些亮灯。